Linear Algebra Gauss Jordan Elimination

[kpx001]

[10 8 4 -116]
[-4 2 -6 54]
[3 -3 1 5]

is there an easy way to solve this without using so many fractions?
i solve for row1 to equal [1 x x x x]
then i get soo many fractions after that.

 

[mmm4444bot]

With such a small system, I do not think that the amount of work is important.

What's important is that you follow the instructions. If you're told to use Gauss Jordan Elimination, then do it.

Are you free to solve this system using any method? (I need to know the answer to this question, before I can consider offering alternate methods.)

With Gauss Jordan Elimination, one can often make strategic choices when deciding which row operations to use. It takes practice to recognize these strategies.

For example, did you start by dividing rows 1 and 2 by 2 to reduce the numbers?

If you're not told to put the matrix into Reduced Row-Echelon Form, then Row-Echelon Form plus backsolving is not too bad. All of the denominators turned out to be 3, for me, so the arithmetic was only adding and subtacting numerators. (You can add stuff like 2/3 + 2 in your head, right?)

Row Echelon Form can be achieved in 5 steps that involve adding fractions, with the other steps not involving any addition of fractions.

Here are these steps.

Divide R1 by 2
Divide R2 by 2
Divide R3 by 3
Swap R1 and R3
Replace R2 with 2 * R1 + R2
Replace R3 with 5 * R1 + R3
Multiply R2 by -1
Replace R3 with -9 * R2 + R3
Multiply R3 by -3/62

Now you're at Row-Echelon Form, and you can read-off the value of z.

Next, you're off to backsolving for y, then for x to finish.

Please show your work, if you want more help with this exercise.